Radiographic imaging, in its simplest expression, is an X-ray beam traversing an object and a detector relating the overall attenuation per ray. The attenuation is derived from a comparison of the same ray with and without the presence of the object. From this conceptual definition, several steps are required to properly construct an image. For instance, the finite size of the X-ray generator, the nature and shape of the filter blocking the very low energy X-ray from the generator, the details of the geometry and characteristics of the detector, and the capacity of the acquisition system are all elements that affect how the actual reconstruction is performed. In the reconstruction, the map of the linear attenuation coefficient (LAC) of the imaged subjects is obtained from the line integrals of the LAC through an inverse Radon transform. The line integrals can be related to the logarithm of the primary intensity of the X-rays passing through the subject. However, the measured X-ray intensity on the detector may include both scattering photons and primary photons. Thus, the images reconstructed from scattering may contain some scattering artifacts.
Many clinical applications can benefit from spectral CT technology, which can provide improvement in material differentiation and beam hardening correction. Further, semiconductor-based photon-counting detectors are a promising candidate for spectral CT, which is capable of providing better spectral information compared with conventional spectral CT technology (e.g., dual-source, kVp-switching, etc.).
Due to the dead time (˜100 ns), which is determined by the type of semiconductor (e.g. CZT or Cd Te), its thickness and readout circuitry, pulse pileup at high X-ray flux (˜10 8 cps/mm2) can be very severe, and the measured spectral signals can be distorted. The distorted spectral signal can cause artifacts in the reconstruction of images. If the pileup effect can be corrected in the detector model, the image quality can be improved. However, computing the detector's response while accounting for pileup correction results in significant usage of computational resources of the CT system, and moreover makes the process of determining the response of the photon-counting detector time-intensive.
Accordingly, an efficient technique for reducing computational time required in computing a response of the photon-counting detector is desired.